On the honeycomb conjecture for Robin Laplacian eigenvalues
Optimization and Control
2017-07-03 v1 Analysis of PDEs
Spectral Theory
Abstract
We prove that the optimal cluster problem for the sum of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity.
Cite
@article{arxiv.1706.10055,
title = {On the honeycomb conjecture for Robin Laplacian eigenvalues},
author = {Dorin Bucur and Ilaria Fragala},
journal= {arXiv preprint arXiv:1706.10055},
year = {2017}
}